It seems that after some investigation I am in a position to answer my own
questions, so I am following up my earlier message in case anyone is
interested.
On Tue, 10 Jan 2012 22:09:19 -0000, Oleksandr Rasputinov
<oleksandr_rasputinov at hmamail.com> wrote:
> 1. We know that some possible values for the "PostProcess" option are
> "KKT", "InteriorPoint", and FindMinimum (with the undocumented Method
> suboption giving access to a rather wide range of possibilities). Are
> there any others?
No. (Except Automatic, which means either "KKT" or "InteriorPoint", or
both, in either order, depending on the value of
Optimization`NMinimizeDump`$PostprocessOrder.)
> And is there any difference between the option values "InteriorPoint"
> and {FindMinimum, Method -> "InteriorPoint"}?
Different code paths are followed in setting up the minimization, but the
same core algorithm is used in both cases.
> 2. For the "DifferentialEvolution" method, the documentation states that
> recombination is according to Storn and Price's rand/1 scheme. Are any
> other schemes implemented?
No. Actually even the rand/1 implementation is not done "correctly" (i.e.
per the description given by Storn and Price) as the vectors chosen for
recombination are picked completely at random, whereas strictly speaking
differential evolution requires them to be mutually different as well as
different from the base vector (i.e. the one they compete against in the
selection tournament). The difference will not matter for a large enough
number of search points, but may lead to misconvergence in some cases.
Also, the documentation states that differential evolution is
computationally intensive, which (as the algorithm is very simple and can
be expressed efficiently in terms of array operations) could be taken to
refer to the fact that it requires a large number of function evaluations
compared to local search methods. However, finding on closer inspection
that the implementation is done in an (in my opinion, inappropriate)
procedural style and with little attention to efficiency, I now suspect
that this is the real reason for its relatively poor performance. This is
unfortunate given the strong potential of differential evolution for
heavy-duty minimization problems, but perhaps it will be addressed in the
future.